Use properties of logarithms to write each expression as a sum or difference of logarithms. Assume that variables represent positive real numbers.
-$\log _{8} x y^{2}$
A) $2 \log _{8} x-\log _{8} y$
B) $\log _{8} \mathrm{x}+2 \log _{8} \mathrm{y}$
C) $\log _{4} x+\log _{4} y$
D) $2 \log _{4} x-2 \log _{4} y$

Question

Quizplus · Accepted Answer

The correct answer is B because according to the properties of logarithms, $\log_b(xy) = \log_b x + \log_b y$ and $\log_b(x^n) = n \log_b x$. Applying these properties to $\log_8(xy^2)$ results in $\log_8 x + 2\log_8 y$.

Use Properties of Logarithms to Write Each Expression as a Sum